The present invention relates to a pressure transducer for sensing a pressure or a differential pressure, and more particularly to a pressure transducer of the capacitive type which utilizes a single crystal of silicon etched to form a diaphragm as one electrode of the transducer with other silicon plates mounted parallel to it to carry other fixed electrodes. The present invention also relates to means for mounting pressure transducers of this type.
Pressure transducers of the type described above are subject to changes in calibration, both in zero and span, when there is a change in the dimensions of the parts of the transducer and/or the mounting structure such as may result from changes in the temperature or the hydrostatic pressure of the medium surrounding the transducer and its mounting. These changes in dimension may cause a distortion of the shape of the transducer so as to distort the diaphragm and cause a change in the zero of the transducer calibration. However, even if the nature of the structure is such that distortion is avoided, changes may occur in the linear dimensions so that the transducer diaphragm is subjected to a change in radial stress causing a change in the span of the transducer calibration. These effects may, of course, combine so that there is both a distortion of shape causing a change in the zero and a change in linear dimensions causing a change in the span. Both effects are, of course, particularly noticeable when the transducer is used to measure small pressure differentials in a line operating at a high pressure with wide temperature swings, as will frequently occur in industrial processes. For example, it may be necessary to measure a 1 psi differential in a line at 10,000 psi with temperature swings amounting to something on the order of 100.degree. F.
Pressure transducers using silicon diaphragms as described above are shown in U.S. Pat. No. 4,257,274 where FIGS. 4 and 6 show capacitive pressure transducers having etched silicon diaphragms mounted between silicon plates with the spacing between the diaphragm and the plates being determined by borosilicate glass spacer rings. These rings serve to provide the necessary electrical isolation between the diaphragm and the plates as well as the material necessary for anodically bonding the plates to the diaphragm. This reference does not disclose any means for minimizing the effects of changes in temperature or hydrostatic pressure. In addition the structure of the disclosed transducer is such that it would be difficult to accurately predetermine the spacing between the diaphragm and the plates, for the glass spacer could not be accurately dimensioned without using expensive procedures of manufacture. This spacing is very important in capacitive transducers.
Another pressure transducer using a silicon diaphragm is shown in U.S. Pat. No. 4,364,276. This transducer is not of the capacitive type, but instead is of the type which uses a vapor deposition or a diffusion type strain gauge on the diaphragm to provide the pressure measurement. This transducer, however, is of interest since it describes a mounting means alledgedly designed to minimize the effects of Young's modulus on the pressure measurement. In this patent, FIG. 6, for example, shows a silicon diaphragm mounted on a thin glass washer which is in turn mounted on a metal support member having a Young's modulus which is substantially equal to that of silicon. The patentee states that the strain produced in the diaphragm due to the differences in the Young's modulus of glass and silicon can be minimized by this structure. It is evident from this disclosure that the patentee was only attempting to prevent the distortion of the diaphragm to avoid changes in the zero with changes in hydrostatic pressure. No attempt is made to solve the problem of change in the span due to changes in radial stress in the diaphragm as will result from dimension changes alone. The patentee is only attempting to balance the effect of the mounting on one side of the glass washer with the effect of the silicon on the other side so that there will be no net distortion resulting from changes in hydrostatic pressure.
As mentioned above, it is important to accurately determine the spacing between the electrodes of a capacitive pressure transducer during manufacture in a way which is inexpensive and yet one which will cause all of the transducers manufactured to exhibit substantially the same response characteristics. This spacing problem does not exist with strain gauge or other types of transducers. Therefore, the means for minimizing the effects of the elastic moduli on the transducer in the disclosure of U.S. Pat. No. 4,364,276 did not need to minimize variations in spacing.
The problems which arise because of changes in the hydrostatic pressure surrounding the transducer and its mounting result from the use of materials with different elastic moduli. Thus, the borosilicate glass normally used to provide anodic bonding of a silicon diaphragm to silicon electrode support plates creates a problem since its Young's modulus is different from that of the silicon diaphragm and silicon plates. As a result of this difference, an increase in the hydrostatic pressure of the transducer's surroundings will cause a decrease in the volume of each of the individual parts of the transducer subjected to this change in pressure. Normally all of the parts are exposed to this change, including the parts used to provide a firm mounting of the transducer. Since only the change in the radial dimensions of the diaphragm are a cause of trouble, changes in thickness of the diaphragm and the plates need not be considered.
To consider the magnitude and nature of the problem presented by differences in the Young's modulus of the materials of the transducer, it is necessary to consider the pressure-deflection relationship of a clamped and tensioned diaphragm. This relationship is as follows: EQU P=[(16EW.sub.0 h.sup.3)/(3(1-v.sup.2)a.sup.4)]+[4T.sub.0 W.sub.0 h/a.sup.2 ](1)
where:
E=Young's modulus PA1 v=Poisson's ratio PA1 h=thickness of the diaphragm PA1 a=diaphragm radius PA1 W.sub.0 =center of deflection PA1 T.sub.0 =radial stress PA1 (1) temperature change, if the thermal expansion coefficients differ for the materials, and PA1 (2) hydrostatic pressure change, if the Young's moduli are different. PA1 E.sub.1 =Young's modulus of the first material PA1 E.sub.2 =Young's modulus of the second material PA1 .alpha..sub.1 =thermal expansion coeff. of first material PA1 .alpha..sub.2 =thermal expansion coeff. of second material PA1 .DELTA.T=temperature change PA1 .DELTA.p=hydrostatic pressure change PA1 A.sub.1 =cross sectional area of first material PA1 A.sub.2 =cross sectional area of second material
The first bracketed expression of equation (1) expresses the relationship due to the clamped nature of the diaphragm and the second bracketed expression expresses the relationship due to the fact that the diaphragm is tensioned.
The percent change in the pressure response (span) of the diaphragm due to radial stress in the diaphragm is given by: EQU % span shift=3/4(1-v.sup.2)(T.sub.0 /E)(a/h).sup.2 .times.100 (2)
In sensors having a symmetrical parallel plate configuration which involves only two different materials (a first material of silicon and a second material of borosilicate glass, for example) such as is shown in FIGS. 4 and 6 of U.S. Pat. No. 4,257,274 and in the present invention, radial stresses in the diaphragm arise due to:
The stress in the first material due to changes in hydrostatic pressure is given by: EQU T.sub.0 =-[.DELTA.P(E.sub.1 -E.sub.2)]/[(A.sub.1 /A.sub.2)E.sub.1 +E.sub.2 ](3)
and the stress in the first material due to changes in temperature is given by: EQU T.sub.0 =-[E.sub.1 E.sub.2 (.alpha..sub.1 -.alpha..sub.2).DELTA.T]/[(A.sub.1 /A.sub.2)E.sub.1 +E.sub.2 ](4)
where:
Since the outside dimensions of all three plates of the sensor are the same, the area ratio A.sub.1 /A.sub.2 can be replaced with a corresponding thickness ratio t.sub.1 /t.sub.2.
It will be evident from an examination of equations (2), (3) and (4) that an equality between the thermal expansion coefficients and the Young's moduli would result in a zero value for the stress T.sub.0 and the % span shift. This condition can, of course, be met by using the same material for all components of the transducer and its mounting. Such a solution to the problem is not possible, however, because of the need to bond the layers of the structure together and to isolate electrically the diaphragm from the electrode support plates. Other approaches must therefore be used to solve this problem.
It is an object of this invention to provide a structure for the pressure transducer and its mounting which will make possible the accurate spacing of the electrodes of a capacitive transducer, while at the same time providing substantial insensitivity of both the span and zero of the device to changes in temperature and hydrostatic pressure.
It is a further object of this invention to provide a mounting structure, which will provide substantial mechanical isolation for the transducer.